Ecuiioinical Expansion in Steam Engines. 35o 



XX. — Note relating to a Newly- Discovered Absolute Limit to 

 Economical Expansion in Steam-Engines. 



BY ROBERT H. THURSTON. 



Bead October 2d, 1882. 



Note. — This paper was prepai-ed in the latter part of April, 1882, and 

 sent to the Academy for presentation. But an accidental non-delivery 

 prevented its reaching the Committee on Papers and Publication, until too 

 late for reading before the meetings -vvere suspended for the summer. It 

 was, therefore, i^resented at the first meeting of the autumn ; but its actual 

 date of reading is really several months later than it should properly have 

 been. 



D. S. M. 



A paper "On the Behavior of Steam in the Steam Engine, 

 and on Curves of Efficiency,"* was read by the writer before 

 the New York Academy of Sciences, February 13th, 1882. 



In that paper it was shown that, if a "Curve of Efficiency" 

 were constructed for any steam engine, such that its ordinates 

 should be proportional to the work done by quantities of steam 

 laid down in arithmetical progression as abscissas, — the quantity 

 used at full stroke, i. e., without expansion, being taken as 

 nnity, — that such curve would depart from the curve given by 

 the ideal perfect engine, in character, form and location, and 

 that it could not pass through the origin, as does that of the 

 ideal engine, unless by passing through a point of inflection. 



It was shown that, such a cui-ve being constructed, ratios of 

 expansion at maximum efficiency could be determined by draw- 

 ing tangents to the curve from the junction of the back-jjressure 

 line with the ordinate passing through the origin. It was shown 

 that the ratio so determined is larger as the ratio of initial to 

 back-pressure increases. It is the object of this note to call at- 

 tention to the fact that, for the real engine, there exists an 

 absolute limit to economical expansion for every such engine, 

 which cannot be exceeded, however high the pressure of steam 

 may be carried. 



* Trans. N. Y. Acad. Sci., February, 1882; Journal Franklin Institute, Feb., 1882. 



